The Franke function, which is a weighted sum of four exponentials reads as follows $$ -f(x,y) = \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\begin{align*} +f(x,y) = &\frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} \\ +& - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\end{align*} $$
diff --git a/doc/Projects/2018/Project1/html/Project1-bs.html b/doc/Projects/2018/Project1/html/Project1-bs.html index 07aa51264..3086aff06 100644 --- a/doc/Projects/2018/Project1/html/Project1-bs.html +++ b/doc/Projects/2018/Project1/html/Project1-bs.html @@ -177,7 +177,10 @@ the bootstrap methods, in order to perform a proper assessment of our models.
The Franke function, which is a weighted sum of four exponentials reads as follows $$ -f(x,y) = \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\begin{align*} +f(x,y) = &\frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} \\ +& - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\end{align*} $$
diff --git a/doc/Projects/2018/Project1/html/Project1.html b/doc/Projects/2018/Project1/html/Project1.html index dd7a77c63..74393b12a 100644 --- a/doc/Projects/2018/Project1/html/Project1.html +++ b/doc/Projects/2018/Project1/html/Project1.html @@ -134,7 +134,10 @@ the bootstrap methods, in order to perform a proper assessment of our models.
The Franke function, which is a weighted sum of four exponentials reads as follows $$ -f(x,y) = \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\begin{align*} +f(x,y) = &\frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} \\ +& - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\end{align*} $$
diff --git a/doc/Projects/2018/Project1/ipynb/ipynb-Project1-src.tar.gz b/doc/Projects/2018/Project1/ipynb/ipynb-Project1-src.tar.gz index ee46cfcad..89ca2b675 100644 Binary files a/doc/Projects/2018/Project1/ipynb/ipynb-Project1-src.tar.gz and b/doc/Projects/2018/Project1/ipynb/ipynb-Project1-src.tar.gz differ diff --git a/doc/Projects/2018/Project1/pdf/Project1.p.tex b/doc/Projects/2018/Project1/pdf/Project1.p.tex index 06eb6c25b..d5d47829f 100644 --- a/doc/Projects/2018/Project1/pdf/Project1.p.tex +++ b/doc/Projects/2018/Project1/pdf/Project1.p.tex @@ -180,9 +180,10 @@ the bootstrap methods, in order to perform a proper assessment of our models. The Franke function, which is a weighted sum of four exponentials reads as follows -\[ -f(x,y) = \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. -\] +\begin{align*} +f(x,y) = &\frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} \\ +& - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\end{align*} The function will be defined for $x,y\in [0,1]$. Our first step will be to perform an OLS regression analysis of this function, trying out diff --git a/doc/Projects/2018/Project1/pdf/Project1.tex b/doc/Projects/2018/Project1/pdf/Project1.tex index b572848a0..b341f7631 100644 --- a/doc/Projects/2018/Project1/pdf/Project1.tex +++ b/doc/Projects/2018/Project1/pdf/Project1.tex @@ -150,9 +150,10 @@ the bootstrap methods, in order to perform a proper assessment of our models. The Franke function, which is a weighted sum of four exponentials reads as follows -\[ -f(x,y) = \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. -\] +\begin{align*} +f(x,y) = &\frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} \\ +& - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\end{align*} The function will be defined for $x,y\in [0,1]$. Our first step will be to perform an OLS regression analysis of this function, trying out diff --git a/doc/src/Projects/2018/Project1/Project1.do.txt b/doc/src/Projects/2018/Project1/Project1.do.txt index bef01518b..780c0c1ab 100644 --- a/doc/src/Projects/2018/Project1/Project1.do.txt +++ b/doc/src/Projects/2018/Project1/Project1.do.txt @@ -22,9 +22,10 @@ the bootstrap methods, in order to perform a proper assessment of our models. The Franke function, which is a weighted sum of four exponentials reads as follows !bt -\[ -f(x,y) = \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. -\] +\begin{align*} +f(x,y) = &\frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}+\frac{3}{4}\exp{\left(-\frac{(9x+1)^2}{49} \\ +& - \frac{(9y+1)}{10}\right)}+\frac{1}{2}\exp{\left(-\frac{(9x-7)^2}{4} - \frac{(9y-3)^2}{4}\right)} -\frac{1}{5}\exp{\left(-(9x-4)^2 - (9y-7)^2\right) }. +\end{align*} !et The function will be defined for $x,y\in [0,1]$. Our first step will